大边距低秩张量分析
Large Margin Low Rank Tensor Analysis
AI总结：
本文提出一种监督模型，用于学习高维欧几里得空间中嵌入张量的内在结构，通过固定点延续过程联合发现最优维度和低维嵌入表示，模拟人类大脑的认知过程，并在物体识别和人脸识别中验证其优越性。
摘要：
除了向量表示外，人类认知的直接对象通常是高阶张量，如2D图像和3D纹理。基于此，两个有趣的问题自然产生：人类大脑如何以“流形”方式表示这些张量感知，以及如何在“流形”上进行识别。本文提出一种监督模型，用于学习嵌入高维欧几里得空间中的张量的内在结构。通过固定点延续过程，该模型自动且联合发现最优维度和低维嵌入的表示。这使其成为人类大脑认知过程的有效模拟。此外，基于所学低维嵌入之间相似性的模型推广可视为人类大脑识别的对应物。在物体识别和人脸识别应用中的实验展示了所提模型优于现有方法的优越性。
英文摘要：
Other than vector representations, the direct objects of human cognition are generally high-order tensors, such as 2D images and 3D textures. From this fact, two interesting questions naturally arise: How does the human brain represent these tensor perceptions in a "manifold" way, and how can they be recognized on the "manifold"? In this paper, we present a supervised model to learn the intrinsic structure of the tensors embedded in a high dimensional Euclidean space. With the fixed point continuation procedures, our model automatically and jointly discovers the optimal dimensionality and the representations of the low dimensional embeddings. This makes it an effective simulation of the cognitive process of human brain. Furthermore, the generalization of our model based on similarity between the learned low dimensional embeddings can be viewed as counterpart of recognition of human brain. Experiments on applications for object recognition and face recognition demonstrate the superiority of our proposed model over state-of-the-art approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
